1. Dimensional Analysis Definition
Analysis using the fact that physical quantities added to or equated with each other must be expressed in terms of the same fundamental quantities (such as mass, length, or time) for inferences to be made about the relations between them
Translation - making sure you have all the right units

2. Fractions When multiplying fractions, multiply across
Remember to reduce where possible

3. Conversions
When we convert a measurement with one unit to another, it is easiest to set up ratios
Ex. If 1 ft = 12in, how many inches are in 3 ft?

4. Unit conversion factor
A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.
1 ft
? in.
1 yd
? ft
1 mi
1lb
? oz
1 pt
? c
1 qt
? pt
1 gal
? qt
1 hr
? min
1 min
? s 1m
? cm
1km
? m
Fill in the blanks for as many as you know. Compare with your neighbor.

5. Unit conversion factor
A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.
Ask for some reciprocals so you know they understand.

6. Choose a unit conversion factor that…
Introduces the unit you want in the answer
Cancels out the original unit so that the one you want is all that is left.

7. “Canceling” out Words

8. Practice: Choose the appropriate conversion factor.
Inches to feet
Minutes to hours
Meters to centimeters

9. Use the one that will cancel out the units you want to change
Convert 8 yards to feet…
Make a decision: What conversion factor will you use?
Set up the problem: Multiply the measurement by the conversion factor.
Hint!
Use the one that will cancel out the units you want to change
Solve the problem: Perform the multiplication

10. A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units.
What are the two conversion factors comparing quarts and gallons?
Which one will “cancel” quarts?
16 qt 

11. You Try it!
One bag of apples weighs 64 ounces. How many pounds does it weigh?
Darren drank 2 liters of water. How many milliliters of water did he drink?

12. Convert 80 miles per hour to feet per hour.
Convert 63,360 feet per hour to miles per hour.

13. You Try it! Convert 32 feet per second to inches per second.
A craft store charges $1.75 per foot for lace. How much per yard is this?

14. Word Problems
The average American eats 23 pounds of pizza per year. Find the number of ounces the average American eats per year.
The average American eats 368 ounces of pizza per year.

15. How many seconds in an hour?
Word Problems…
A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? Hint: Set up the words first.
How many seconds in an hour?
Once you’ve determined how many seconds in an hour, decide which conversion factor you should use.
The car traveled 44 feet per second.

16. Let’s try something real hard
What if you can’t convert units directly?
Ex. 8 gallons= ___fl oz

17. Is this what you got?

18. Rate Conversions
What do you do if you have 5ft/sec and you need it in miles/hour?
Same thing as before! Just set up one conversion at a time to keep it simple.

19. Converting Areas
When it comes to converting areas, you have to take into account two dimensions.
Ex. 5 m2=___ cm2
Remember that 5 m2 is the same thing as 5·m·m
What would you do for volume conversions?

20. One more thing…. What needs to be done here: 2 feet 7 inches
Find the area of the rectangle